Introduction to Stochastic Dynamic Programming: Probability and Mathematical
Introduction to Stochastic Dynamic Programming: Probability and Mathematical
The Dynamic and Stochastic Knapsack Problem
Operations Research
A reinforcement learning approach to dynamic resource allocation
Engineering Applications of Artificial Intelligence
Models and Algorithms for Stochastic Online Scheduling
Mathematics of Operations Research
Managing Patient Service in a Diagnostic Medical Facility
Operations Research
Scheduling: Theory, Algorithms, and Systems
Scheduling: Theory, Algorithms, and Systems
A Learning Approach for Interactive Marketing to a Customer Segment
Operations Research
Relaxations of Weakly Coupled Stochastic Dynamic Programs
Operations Research
Markov decision process applied to the control of hospital elective admissions
Artificial Intelligence in Medicine
A Markov decision process approach to multi-category patient scheduling in a diagnostic facility
Artificial Intelligence in Medicine
Lagrangian relaxation and constraint generation for allocation and advanced scheduling
Computers and Operations Research
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We define a class of discrete-time resource allocation problems where multiple renewable resources must be dynamically allocated to different types of jobs arriving randomly. Jobs have geometric service durations, demand resources, incur a holding cost while waiting in queue, a penalty cost of rejection when the queue is filled to capacity, and generate a reward on completion. The goal is to select which jobs to service in each time-period so as to maximize total infinite-horizon discounted expected profit. We present Markov Decision Process (MDP) models of these problems and apply a Lagrangian relaxation-based method that exploits the structure of the MDP models to approximate their optimal value functions. We then develop a dynamic programming technique to efficiently recover resource allocation decisions from this approximate value function on the fly. Numerical experiments demonstrate that these decisions outperform well-known heuristics by at least 35% but as much as 220% on an average.